
Figure 1: Intersection. Click on the image to see a representation of A ∩ B. 

An intersection of two or more
sets
is a set containing the members that are in all of the sets. This is spoken, "Set
C is the intersection of sets
A and B."
This is written, C = A ∩ B.
Properties of Intersection of Sets
Property  Math Statement  Description 
Commutative  A ∩ B = B ∩ A  The intersection of sets is commutative 
Associative  (D ∩ E) ∩ F = D ∩ (E ∩ F)  The intersection of sets is associative 
Distributive  (D ∩ E) ∪ F = (D ∪ F) ∩ (E ∪ F) (D ∪ E) ∩ F = (D ∩ F) ∪ (E ∩ F)  The intersection and union of sets are distributive 
Table 1: Properties of the intersection of two sets. 
